Theorems · Theorem · linear algebra
Matrix.self_mul_conjTranspose_eq_zero
∀ {n : Type u_2} {R : Type u_4} [inst : Fintype n] [inst_1 : PartialOrder R] [inst_2 : NonUnitalRing R]
[inst_3 : StarRing R] [StarOrderedRing R] [NoZeroDivisors R] {m : Type u_5} {A : Matrix m n R},
A * A.conjTranspose = 0 ↔ A = 0- Defined in
- Mathlib.LinearAlgebra.Matrix.DotProduct
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement and proof · cited by 4,303
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- NoZeroDivisorsstatement and proof · cited by 545
- Matrix.extproof · cited by 540
- NonUnitalRingstatement and proof · cited by 422
- Matrix.conjTransposestatement and proof · cited by 202
- Matrix.ext_iffproof · cited by 18
- Matrix.zero_mulproof · cited by 16
- dotProduct_self_star_eq_zeroproof · cited by 1
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